How to Simplify Variable Expressions? (+FREE Worksheet!)

Learn the definition of variable and expression and how to simplify variable expressions.

How to Simplify Variable Expressions? (+FREE Worksheet!)

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Step by step guide to simplifying variable expressions

  • In algebra, a variable is a letter used to stand for a number. The most common letters are: \(x, y, z, a, b, c, m\) and \(n\).
  • An algebraic expression is an expression contains integers, variables, and math operations such as addition, subtraction, multiplication, division, etc.
  • In an expression, we can combine “like” terms. (values with same variable and same power)

Simplifying Variable Expressions – Example 1:

Simplify this expression. \(2x + \ 3x + \ 4=\)\(?\)

Solution:

Combine “like” terms. Then: \(2 x \ + \ 3 x \ = 5x \) (remember you cannot combine variables and numbers).

Then: \(2x + 3 x + \ 4=5x + \ 4\) (remember you cannot combine variables and numbers).

Simplifying Variable Expressions – Example 2:

Simplify this expression. \(12 \ – \ 3x^{2} \ + 5 x + \ 4 x^{2}=\)\(?\)

Solution:

Combine “like” terms: \(- \ 3x^{2} \ + 4 x^{2}=x^{2}\)
Then: \(12 \ – \ 3 x^{2} \ + \ 5x + 4 x^{2}\) \(=12 \ + x^2 + 5x\). Write in standard form (biggest powers first): \(x^2 \ + 5 x + \ 12\)

Simplifying Variable Expressions – Example 3:

Simplify this expression. \((10x+2x+3)=\)\(?\)

Solution:

Combine “like” terms: \((10x+2x)=12x\)

Then: \((10x+2x+3)=12x+3\) (remember you cannot combine variables and numbers).

Simplifying Variable Expressions – Example 4:

Simplify this expression. \(12-3x^2+9x+5x^2=\)\(?\)

Solution:

Combine “like” terms: \(-3x^2+5x^2=2x^2\)
Then: \(12-3x^2+9x+5x^2=12+2x^2+9x\). Write in standard form (biggest powers first): \(2x^2+9x+12\)

Exercises for Simplifying Variable Expressions

Simplify each expression.

  • \(\color{blue}{– 2 – x^2 – 6x^2}\)
  • \(\color{blue}{ 3 + 10x^2 + 2}\)
  • \(\color{blue}{ 8x^2 + 6x + 7x^2}\)
  • \(\color{blue}{5x^2 – 12x^2 + 8x }\)
  • \(\color{blue}{– 2(4 – 6x) – 3x }\)
  • \(\color{blue}{ 9 – 2x + 5x + 2}\)

Download Simplifying Variable Expressions Worksheet

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Answers

  • \(\color{blue}{– 7x^2 – 2}\)
  • \(\color{blue}{10x^2 + 5}\)
  • \(\color{blue}{15x^2 + 6x}\)
  • \(\color{blue}{– 7x^2 + 8x}\)
  • \(\color{blue}{9x \ – 8 }\)
  • \(\color{blue}{3x \ + 11}\)

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